Rosetta
The problem presented in this section is a MGADSM problem relative to a mission to the comet 67P/Churyumov-Gerasimenko. The fly-by sequence selected is similar to the one planned for the spacecraft Rosetta. The objective function considered is the total mission delta V, including the launcher capabilities.
The code
- MATLAB: use the function rosetta.m and pass to it the MGAproblem variable contained in rosetta.mat
- C++: call the function "double rosetta(const std::vector & x)" provided in the GTOPtoolbox.
- C++ (PaGMO): use the class pagmo::problem::rosetta
- Python 2.7 (PyGMO): use PyGMO.problem.rosetta().obj_fun(x)
Problem Description
The box bounds on each of the decision vector variable are given below.
State | Variable | Lower Bounds | Upper Bounds | Units |
|---|---|---|---|---|
| x(1) | t0 | 1460 | 1825 | MJD2000 |
| x(2) | Vinf | 3 | 5 | km/sec |
| x(3) | u | 0 | 1 | n/a |
| x(4) | v | 0 | 1 | n/a |
| x(5) | T1 | 300 | 500 | days |
| x(6) | T2 | 150 | 800 | days |
| x(7) | T3 | 150 | 800 | days |
| x(8) | T4 | 300 | 800 | days |
| x(9) | T5 | 700 | 1850 | days |
| x(10) | eta1 | 0.01 | 0.9 | n/a |
| x(11) | eta2 | 0.01 | 0.9 | n/a |
| x(12) | eta3 | 0.01 | 0.9 | n/a |
| x(13) | eta4 | 0.01 | 0.9 | n/a |
| x(14) | eta5 | 0.01 | 0.9 | n/a |
| x(15) | r_p1 | 1.05 | 9 | n/a |
| x(16) | r_p2 | 1.05 | 9 | n/a |
| x(17) | r_p3 | 1.05 | 9 | n/a |
| x(18) | r_p4 | 1.05 | 9 | n/a |
| x(19) | b_incl1 | -pi | pi | rad |
| x(20) | _incl2 | -pi | pi | rad |
| x(21) | b_incl3 | -pi | pi | rad |
| x(22) | b_incl4 | -pi | pi | rad |
No other constraints are considered for this problem. The objective function is considered to the precision of meters per second.
Solutions:
The best solutions submitted to this problem are listed below in chronological order:
Author | Affiliation | Date | Obj Fun | Solutions | Algo |
|---|---|---|---|---|---|
| T., Vinko, D., Izzo | European Space Agency | March, 2008 | 1.449 km/s | x=[1524.25, 3.95107, 0.738307, 0.298318, 365.123, 728.902, 256.049, 730.485, 1850, 0.199885, 0.883382, 0.194587, 0.0645205, 0.493077, 1.05, 1.05, 1.05, 1.36925, -1.74441, 1.85201, -2.61644, -1.53468] | DE |
| T., Vinko, D., Izzo | European Space Agency | April, 2008 | 1.417 km/s | x=[1524.26, 3.83938, 0.262978, 0.779762, 365.574, 720.579, 262.222, 728.772, 1848.47, 0.194268, 0.225388, 0.273158, 0.671802, 0.407266, 1.61803, 1.06012, 3.33304, 1.08071, -1.32760, 1.85218, -1.44709, -1.97420] | DE + PSO |
| B. Addis, A. Cassioli, M. Locatelli, F. Schoen | Global Optimization Laboratory, University of Florence | May, 2008 | 1.368 km/s | x=[1532.24175527, 4.06829338437, 0.720326051073, 0.0348126697442, 365.2434892, 712.701756835, 260.961096679, 729.491441263, 1850, 0.202466066763, 0.486930227754, 0.356331627668, 0.549883084573, 0.431923236806, 1.28119554825, 1.05000000107, 3.1003448392, 1.0841556867 -1.97835856005, 1.81131692678, -1.26622621813, -1.97940868135] | MBH |
| M. Vasile, E. Minisci | University of Glasgow | Sept, 2008 | 1.360 km/s | x=[1543.30669582458, 4.62591297553792, 0.735711649721644, 0.751372228132414, 365.24128038597, 704.776990594467, 258.110840823509, 730.484771806871, 1849.99995454174, 0.341009328525255, 0.808663668992205, 0.376496220185218, 0.171287567923826, 0.431489206122146, 3.07135208604219, 1.06000000320681, 1.41824842842757, 1.39748724339122, -1.39587494176148 1.77647871470111, -2.52771948343642, -1.58247504575273] | -- |
| M. Vasile, E. Minisci | University of Glasgow | Sept, 2008 | 1.355 km/s | x=[1541.2778574301 4.41425813939918 0.738120308957349 0.565680439091451 365.240617831587 708.567754159261 258.093449382336 730.090210655871 1850 0.270070640549605 0.807410043318084 0.0340763968862974 0.665797649174603 0.439110068689427 2.98093380724754 1.06 3.22629172773521 1.06 -1.69972011825889 1.79541928084097 -1.55821584701606 -1.97742285404074] | -- |
| B. Addis, A. Cassioli, M. Locatelli, F. Schoen | Global Optimization Laboratory, University of Florence | Oct., 2008 | 1.344 km/s | x=[1543.32709193 4.5134580971 0.728163430778 0.083363202293 365.241449354 707.419993725 257.129520623 730.483802497 1849.96966072 0.31440923274 0.803777352667 0.0321377696745 0.123194720658 0.432626759733 1.4649721658 1.05000000002 3.18319943186 1.05823552668 -2.15517168796 1.78540451293 -1.63643821124 -1.98027492278] | MBH |
| M. Vasile, E. Minisci | University of Glasgow | Oct., 2008 | 1.343 km/s | x=[ 1542.80272275624 4.47844417111601 0.731698680164396 0.878289696281778 365.242313115732 707.754644446782 257.323851633799 730.483723605649 1850 0.469187103696963 0.810371727143097 0.0572409393084966 0.123333368519021 0.436535683460624 2.65762617428421 1.05 3.19780616934668 1.05622179187182 -1.2538881176403 1.78760232965523 -1.59467141651773 -1.97732549500432] | -- |